A Denjoy–Wolff theorem for Hilbert metric nonexpansive maps on polyhedral domains

DOI10.1017/S0305004107000199zbMath1127.47048OpenAlexW2058089778MaRDI QIDQ3594415

Brian Lins

Publication date: 8 August 2007

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004107000199

zbMATH Keywords

nonexpansive mapomega limit setHilbert metricpolyhedral domain

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Fixed points and coincidences in algebraic topology (55M20)

Related Items (10)

Normal Cones and Thompson Metric ⋮ Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones ⋮ A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces ⋮ A unified approach to nonlinear Perron-Frobenius theory ⋮ Denjoy-Wolff theorems, Hilbert metric nonexpansive maps and reproduction-decimation operators ⋮ Hilbert geometry for convex polygonal domains ⋮ The Hilbert metric on Teichmüller space and earthquake ⋮ Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces ⋮ Asymptotic behavior of nonexpansive mappings in finite dimensional normed spaces ⋮ Continuity of the cone spectral radius

Cites Work

• From max-plus algebra to nonexpansive mappings: A nonlinear theory for discrete event systems.
• Hilbert's projective metric on cones of Dirichlet forms
• Iterated linear maps on a cone and Denjoy-Wolff theorems
• Non-expanding maps and Busemann functions
• Extensions of Jentzsch's Theorem
• Linear Operators in Complete Positive Cones
• Iteration of order preserving subhomogeneous maps on a cone
• Iteration of Contractions and Analytic Maps
• The dynamics of contractions

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